power system stabilizers for the synchronous generator

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Power System Stabilizers for The Synchronous Generator Tuning and Performance Evaluation Master of Science Thesis A NDREA A NGEL Z EA Department of Energy and Environment Division of Electric Power Engineering C HALMERS U NIVERSITY OF T ECHNOLOGY G¨oteborg, Sweden 2013 Power System Stabilizers for The Synchronous Generator Tuning and Performance Evaluation ANDREA ANGEL ZEA Department of Energy and Environment Division of Electric Power Engineering CHALMERS UNIVERSITY OF TECHNOLOGY G¨oteborg, Sweden 2013 Power System Stabilizers for The Synchronous Generator Tuning and Performance Evaluation ANDREA ANGEL ZEA c ANDREA ANGEL ZEA, 2013 Department of Energy and Environment Division of Electric Power Engineering Chalmers University of Technology SE–412 96 G¨oteborg Sweden Telephone +46 (0)31–772 1000 Chalmers Bibliotek, Reproservice G¨oteborg, Sweden 2013 Power System Stabilizers for The Synchronous Generator Tuning and Performance Evaluation ANDREA ANGEL ZEA Department of Energy and Environment Division of Electric Power Engineering Chalmers University of Technology Abstract The electromechanical oscillations damping through the synchronous generator is analyzed in this work Traditionally, this has been achieved using a conventional Power System Stabilizer PSS controller, which has the aim of enhancing the dynamic stability of the generator through the excitation control system, therefore a PSS tuning methodology is developed and tested Moreover, other damping control alternative for the synchronous generator based on signal estimation theory is proposed in this thesis Initially, a detailed modelling of the Synchronous Machine Infinite Bus SM-IB system has been accomplished in order to study the electromechanical interaction between a single generator and the power system The SM-IB system model is the base to analyze and to tune the PSS controller It was concluded that it is not necessary to include the damper windings dynamics in the system phase lag analysis since, in the PSS frequency range of interest, the biggest phase lag difference including them was about 10◦ This difference could be considered not sufficient to include the sub-transient model in the PSS tuning analysis Therefore, the linearized transient model of the system is a suitable model for the tuning process Secondly, the main concepts for a PSS tuning methodology, which is based on linear control system theory, are established Specifically, frequency response techniques are used to define the setting for the lead lag filters time constants and PSS gain This is supported on the fact that the predominant trend in the industry is still to use frequency response based tuning methods [12], even more in the case of PSS providers who should tune the controller having detailed information about the generator but not exact details about the connecting grid The methodology is implemented as a software tool in Matlab/Simulink R2011b using the mathematical model of the excitation system provided by the company VG Power AB and giving the option to chose between static and rotating type of exciters; it is also designed considering the rotor speed change as input signal to the PSS The performance of the PSS with the achieved tuning is validated via simulations in the complete SM-IB system model Furthermore, a sensitivity analysis of the local oscillation mode damping to changes in the system operating point is carried out verifying the robustness of the tuning process In all analyzed cases, the minimum damping of the local mode was never less than 10% Finally, the application of a Phasor Power Oscillation Damping POD controller to the excitation control system in the synchronous generator is studied Nowadays, POD for inter-area oscillation modes in power systems is also achieved through FACTS Control structures using low-pass filter based and recursive least square based estimation methods to extract the oscillatory component of a signal has been successfully applied to control FACTS [3], [17] and [5] achieving damping The same idea is used in this work to define an alternative controller for the generator which is based on a low-pass filter based signal estimation algorithm The analysis is done again using the SM-IB system The obtained results indicate that the alternative controller is able to damp successfully the local oscillation mode that appear after applying a disturbance to the system However, deeper studies are needed in order to be able to compare fairly the performance of the PSS and the Phasor POD controller when they are applied to the synchronous generator Additionally, the proposed control approach should be test in a power system model of higher order These are recommended topics for future work Index Terms: Synchronous Generator, PSS Tuning, Signal Estimation, Phasor POD Controller Acknowledgements I would like to express my gratitude to: Massimo Bongiorno and Stefan Lundberg Thanks for your guidance and shared knowledge during this master thesis Also for the interesting courses given during the master program! Mats Wahlen and VG Power AB Thanks for offering a topic of my complete interest and for the opportunity to have a contact with the Swedish industry! Mebtu Beza Many thanks for your support and help! Hector Botero Thanks for your teachings and your example! Colfuturo Thanks for the Scholarship! Chalmers and The Government of Sweden Thanks for the IPOET Scholarship! Diana and Panos Thanks for your company and friendship during this two years in Sweden! Mam´a Aqu´ı se cumple no s´olo mi sue˜no, sino el sue˜no que sembraste en m´ı! Gracias a t´ı por siempre y por todo! Esperanza Tendr´as un vuelo eterno en mi coraz´on! Pap´a, Olga, Sebas, Benja, Familia y Amigos Gracias por estar a mi lado! Andrea Angel Zea G¨oteborg, Sweden, 2013 Acronyms AVR Automatic Voltage regulator PSS Power System Stabilizer SM-IB Synchronous Machine - Infinite Bus POD Power Oscillation Damping FACTS Flexible AC Transmission System TCSC Thyristor Controlled Series Capacitor AC Direct Current DC Direct Current PI Proportional and Integral LMI Linear Matrix Inequality LPF Low-Pass Filter Chapter Acronyms Chapter PSSVG 1.0 Software Tool Fig 5.4 Block Diagram Model Under the Mask 5.3 How to Run a Case An example step by step about how to run a case for PSS tuning is presented as follows: Open the folder ModalFrequencyTuning, where the user can find the main algorithm files Open the file SMIBPar and fill on it the required system parameters Observe that XT , XL , P , Q and the type of exciter are parameters that not need to be input in the file since they will be asked when the program is running As is presented in Fig 5.5, right click to the file MainProgram and select the option ”run” Fig 5.5 Run the Main Algorithm In the command window, the user is asked to define the tuning operation point and the type of exciter as can be seen in Fig 5.6 Fig 5.6 Defining Tuning Operation Point 5.3 How to Run a Case Once the user has input the data, the program display the eigenvalue and phase analysis of the system without PSS and asks the user to input the objective system phase at the analyzed frequency and the lead lag filters tuning type Then the filters time constants are displayed in the command window A root locus plot of the system will pop up in a new window as it is shown in Fig 5.7 The user should analyze the plot and input the selected gain for the PSS in the command window Fig 5.7 Root Locus Plot Window After the gain has been input, the following results are displayed in the command window: • Gain and Phase Margins • System phase limits at the PSS frequency range 0.1 Hz - Hz • Eigenvalue analysis of the system with PSS • Synchronizing and damping torque coefficients at analized oscillation frequency A group of plots as the PSS Bode diagram, the Bode diagram of the system without PSS and with PSS, the system phase in the frequency range of interest and the system zero-pole map will pop up in several windows as is shown in Fig 5.8 and Fig 5.9 These plots help the user to analyze the particular case together with the numerical results Fig 5.8 Result Plots Windows Left: PSS Bode Diagram Right: System Bode Diagram with and without PSS Chapter PSSVG 1.0 Software Tool Fig 5.9 Result Plots Windows Left: Compensated System Phase Lag Right: System Zero-Pole Map At the end, the program asks if the user wants to save the final tuning in a mat file 10 Finally, after analyzing the results about damping, torque coefficients, phase and gain margins and compensated system phase lag, the user should decide if keep the tuning or change any of the input data to run the process again for a new case 5.4 Numerical Results in The Command Window The complete numerical results are display in the command window as is presented in Fig 5.10 The command window can be printed as a pdf file to generate a separate file with the results 5.4 Numerical Results in The Command Window Fig 5.10 Command Window Displayed Numerical Results Chapter PSSVG 1.0 Software Tool 5.5 Program for Tuning at a Different Oscillation Frequency An additional folder called SpecificFrequencyTuning can be found in the main folder of the software tool In this folder are the files of the algorithm to tune the lead lag filters for a different oscillation frequency This algorithm follows the same logic and steps as the main algorithm Also, the same Simulink models are used In this case, the main file that should be run is called OtherFrequencyTuning as is presented in Fig 5.11 Fig 5.11 Run the Alternative Algorithm During the execution process, the program ask the user to input the frequency for analysis as is presented in the example of the Fig 5.12 The system phase lag at that frequency is displayed in the command window and should be consider to define the objective system phase at the analyzed oscillation frequency Fig 5.12 Asking to Input Frequency for Anlaysis Finally, with the previous information the program asks the user to chose the lead lag filters tuning type and follows the same steps as in Section 5.3 for the rest of the tuning process and results 5.6 Comments and Tuning Tips Some aspects to be taken into account about the software tool and the tuning task are listed below: • The objective system phase at analyzed frequency is programmed as to be always negative, this means to obtain undercompensation When the value is asked during the tuning process, it can be input positive or negative but the program will always assume that the objective system phase is a negative value Therefore, it is not possible to tune the lead lag filters overcompensating the system phase for the analyzed frequency • The lead lag filter time constants are tuned to be equal for all filters, more advanced tuning algorithms would be needed to tune each filter in the cascade link with a different purpose In that case, it would be possible to get a desired compensation not only for an specific frequency but for a range of frequencies 5.6 Comments and Tuning Tips • There is not representative difference in the results obtain between the two lead lag filters tuning methods presented in Chapter For Method 2, the program has an internal value for Kf equal to This filter gain should not be modified, furthermore it must not be less than or more than 10 The effect of varying it is to move the compensation central frequency of the filter The higher Kf the more phase lead the compensated system will have at low frequencies badly influencing the synchronizing torque at those frequencies Also the higher Kf the smaller the PSS gain Ks1 should be to guarantee the system stability • Generally, it was observed that the system phase lag is higher when the excitation system use a rotating exciter, this means that the PSS should compensate a higher angle However, as was discussed in Chapter in the synchronizing and damping torque coefficient analysis for this type of exciter, the damping coefficient due to the excitation system is always possitive, this condition support choosing more undercompensation in cases with this kind of exciters • According to many system root locus plot analysis for different levels of phase compensation, it was observed that the less the PSS compensation angle θpss the higher the optimal PSS gain Ks1 can be, introducing higher level of damping • It is consider that a damping of 5% for an oscillation mode is acceptable to not risk the system stability, however there is not an standardised criteria presented in the literature for the required damping in a power system Additionally, it should be taken into account that the gain and phase margins should be positive at the frequency range of interest Also, the obtained PSS tuning should produce positive synchronizing and damping torque coefficients to the system due to the PSS • Finally, the tool needs to be tested for different systems considering several kind of synchronous generator design connected to different external grids, in order to be able to evaluate and validate the results Chapter PSSVG 1.0 Software Tool Chapter Conclusions and Future Work 6.1 Conclusions Based on the literature review, the performed analysis, and the simulations results it is possible to conclude that: • The synchronous machine rotor oscillations due to lack of damping torque can be seen as a small signal stability problem [11] In that case, a linearized model of the SM-IB can provide good representation of the dynamic response of the system to analyze the damping effect that a PSS can introduce • It is not necessary to include the damper windings dynamics in the PSS tuning analysis because the additional phase lag introduced by the sub-transient characteristic is not relevant compared with the increase in mathematical dimension of the system If the small phase lag difference wants to be taken into account, it is possible to treat it as a PSS design criteria which makes to increase the compensation angle some few degrees For the analyzed machine, in the PSS frequency range of interest, the biggest phase lag difference including the damper windings dynamics was about 10◦ This difference could be considered not sufficient to include the sub-transient model in the PSS tuning analysis • The results show how the excitation system may negatively impacts the synchronizing and damping torque components Specifically, for the analized machine, the damping torque coefficient using static exciter with high active power and weak external connecting grid reaches values about -2 p.u Therefore, it is mathematically demonstrated also the need of a PSS to increase the damping torque component specially in the case of excitation systems with static exciters and at low frequencies • A PSS tuning methodology, which is based on linear control system theory, is established in this work Specifically, frequency response techniques are used to define the setting for the lead lag filters time constants and PSS gain This is supported on the fact that the predominant trend in the industry is still to use frequency response based tuning methods [12] • The performance of the PSS with the achieved tuning is validated via simulations in the complete SM-IB system model Furthermore, a sensitivity analysis of the local oscillation mode damping to changes in the system operating point is carried out verifying the robustness of the tuning process The sensitivity analysis is also extended to a PSS tuning performed for an oscillation frequency different than the natural local oscillation mode and once again good damping levels of the local mode are achieved, fact that confirms the reliable tuning In all analyzed cases, the minimum damping of the local mode was never less than 10% • The idea of applying control structures based on signal estimation theory to FACTS to damp oscillations in the power system has been used in this work to define an alternative controller for the generator This controller is based on a low-pass filter based signal estimation algorithm The obtained results indicate that the alternative controller is able to damp successfully the local oscillation mode that appear after applying a disturbance to the SM-IB system Chapter Conclusions and Future Work • A critical comparison between the PSS and the Phasor POD controller reveals several advantages of the Phasor POD controller in aspects as speed of action, robustness, tuning requirements and possibility of parameters adaptation However, the industry still prefer the conventional stabilization based on lead lag filters and the reason could be that acceptable results are obtained with a relative easy way on tuning Also, because more research is needed to guarantee the stability of the system when another control structure or technique is applied with the same aim [4] 6.2 Future Work Based on the obtained results, it is recommended to continue in the following working lines: • PSS tuning algorithm improvement including optimization to expand the performance requirement to a frequency range, which should be the PSS frequency range of interest Some proposed objective functions are the square error between the objective system phase and the real phase of the compensated system, or the square error between a objective oscillation mode damping and the real achieved damping • Deeper analysis of the Phasor POD controller applied to synchronous generator in aspects as its impact on the system stability and on the synchronizing torque component of the machine Additionally, to study the controller in a higher order power system model where inter-area oscillations can be reproduced and more complex dynamic interactions appear allowing to test the controller limits of performance This will also lead to the possibility of a stronger comparison between the PSS and the Phasor POD controller References [1] IEEE Recommended Practice for Excitation System Models for Power System Stability Studies, Std 421.5 2005 ed., IEEE Power Engineering Society 2005 ¨ [2] L Angquist and M Bongiorno, “Auto-normalizing phase-locked loop for grid-connected converters,” IEEE Energy Conversion Congress and Exposition ECCE, pp 2957–2964, September 2009 ¨ [3] L Angquist and C Gama, “Damping algorithm based on phasor estimation,” Power Engineering Society Winter Meeting IEEE, vol 3, pp 1160–1165, 2001 [4] A Ba-muqabel and M Abido, “Review of conventional power system stabilizer design methods,” GCC Conference IEEE, March 2006 [5] M Beza, “Control of energy storage equipped shunt-connected converter for electric power system stability enhancement,” Licentiate of Engineering Thesis, Chalmers University of Technology, Department of Energy and Enviroment, Gothenburg, Sweden, May 2012 [6] M Beza and M Bongiorno, “Power oscillation damping controller by static synchronous compensator with energy storage,” Energy Conversion Congress IEEE, pp 2977–2984, September 2011 [7] J Bladh, “Hydropower generator and power system interaction,” Ph.D Thesis, Uppsala University, Department of Engineering Sciences, Electricity, Uppsala, Sweden, November 2012 [8] M Bongiorno, “Power electronic solutions for power systems lecture 3: Tools for analysis and control of power converters,” Department of Energy and Enviroment, Chalmers University of Technology, Department of Energy and Enviroment, G¨oteborg, Sweden, Tech Rep., 2012 [9] F Demello and C Concordia, “Concepts of synchronous machine stability as affected by excitation control,” Power Apparatus and Systems, IEEE Transactions on PAS88, no 4, p 316 to 329, April 1969 [10] W Heffron and R Phillips, “Effects of modern amplidyne voltage regulator in underexcited operation of large turbine generators,” AIEE Transactions, vol PAS-71, pp 692–697, August 1952 [11] P Kundur, Power System Stability and Control Palo Alto,California: Electric Power Research Institute, 1994 [12] P Kundur and Others, “A pss tuning toolbox and its applications,” Power Engineering Society, General Meeting, vol 4, pp 2090–2094, July 2003 [13] ——, “Application of power systems stabilizers for enhancement of overall system stability,” IEEE Transactions on Power Systems, vol 4, no 2, pp 614–626, May 1989 [14] E Larsen and D Swann, “Applying power system stabilizers part i: General concepts,” IEEE Transactions on Power Apparatus and Systems, vol PAS-100, no 6, pp 3017–3024, June 1981 [15] ——, “Applying power system stabilizers part ii: Performance objectives and tuning concepts,” IEEE Transactions on Power Apparatus and Systems, vol PAS-100, no 6, pp 3025–3033, June 1981 [16] ——, “Applying power system stabilizers part iii: Practical considerations,” IEEE Transactions on Power Apparatus and Systems, vol PAS-100, no 6, pp 3034–3046, June 1981 References ¨ [17] H Latorre and L Angquist, “Analysis of tcsc providing damping in the interconnection colombiaecuador 230 kv,” Power Engineering Society General Meeting, IEEE, vol 4, pp 2361–2366, July 2003 [18] J Machowski and Others, Power System Dynamics: Stability and Control Wiley & Sons, Ltd, 2008 United Kingdom: John [19] A Murdoch and Others, “Integral of accelerating power type pss,” IEEE Transactions on Energy Conversion, vol 14, no 4, pp 1658–1662, December 1999 [20] K Ogata, Modern Control Engineering Fourth Edition New Jersey: Prentice Hall, 2002 [21] O Samuelsson, “Power system damping: Structural aspects of controlling active power,” Ph.D Thesis, Lund Institute of Technology, Lund, Sweden, 1997 [22] S Yee, “Coordinated tuning of power system damping controllers for robust stabilization of the system,” Ph.D Thesis, University of Manchester, Faculty of Engineering and Physical Sciences, Manchester, England, October 2005 Appendix A System Parameters The parameters of the synchronous generator and excitation system used for the calculations and simulations in all chapters of this work were provided by VG Power AB and they are listed as follows A.1 Synchronous Generator Table A.1: Synchronous Generator Parameters Parameter Value Unit Nominal Apparent Power Sn 69 [MVA] Nominal Voltage Vn 13.8 [kV] Inertia Constant H [s] Frequency f 50 [Hz] Damping Torque Coefficient KD [p.u/p.u] Stator Resistance Rs 0.0033 [p.u] d-axis Stator Inductance Lsd 1.177 [p.u] q-axis Stator Inductance Lsq 0.772 [p.u] Stator Leakage Inductance Lsλ 0.174 [p.u] 6.596 [s] 0.324 [s] d-axis Damper Winding Leakage Inductance L1dλ 0.17879 [p.u] q-axis Damper Winding Leakage Inductance L1qλ 0.20104661 [p.u] q-axis Damper Winding Leakage Inductance L2qλ [p.u] Field Resistance Rf d 0.00056937 [p.u] d-axis Damper Winding Resistance R1d 0.02462133 [p.u] q-axis Damper Winding Resistance R1q 0.02768629 [p.u] q-axis Damper Winding Resistance R2q [p.u] ′ d-axis Open Circuit Transient Time Constant Td0 d-axis Stator Transient Reactance ′ Xsd Appendix A System Parameters A.2 Excitation System Table A.2: AVR and Exciter Parameters Value Parameter Unit AVR Proportional Gain Kp 20 [p.u] AVR Integral Gain Ki 0.2 [p.u] Terminal Voltage Transducer Time Constant Tr 0.01 [s] Time Constant due to type of AVR T4 0.004 [s] Power Converter Positive Ceiling Voltage V R M ax [p.u] Power Converter Negative Ceiling Voltage V R M in −3 [p.u] Maximum Integral Control Action Voltage V l M ax [p.u] Minimum Integral Control Action Voltage V l M in −3 [p.u] Maximum Proportional Control Action Voltage V p M ax 10 [p.u] Minimum Proportional Control Action Voltage V p M in −10 [p.u] Table A.3: Parameters Depending on the Type of Exciter Value Parameter Rotating Static Unit Derivative Gain Kd −5 [p.u/p.u] Derivative Filter Time Constant Td [s] Rotating Exciter Gain Ke 1 [p.u/p.u] Rotating Exciter Time Constant Te 0.9 [s] Saturation Function for Rotating Exciter Se 0 [-] Appendix B Transformations Equations for 3-Phase Systems The transformations from 3-phase system to αβ system which is a stationary reference frame, and to dq system which is a rotating reference frame, are presented in the following equations In this case, zero sequence is not considered since the assumption of a symmetric or balanced system is made [8] B.1 Power Invariant 3-phase to αβ Transformation s(t) = sα (t) + jsβ (t) = sα sβ =   (s1 (t)ej0 + s2 (t)ej2π  2  s1  s2  = s3 − √2  2   3 1 − − + s3 (t)ej4π   s1 − √2   s2   − s3 √0 √ −      sα sβ ) (B.1) (B.2) (B.3) B.2 αβ to dq Transformation From αβ to dq v (dq) (t) = v (αβ) (t)e−jθ(t) vd (t) vq (t) = cos(θ) sin(θ) − sin(θ) cos(θ) (B.4) vα (t) vβ (t) (B.5) Appendix B Transformations Equations for 3-Phase Systems From dq to αβ v (αβ) (t) = v (dq) (t)ejθ(t) vα (t) vβ (t) = cos(θ) − sin(θ) sin(θ) cos(θ) (B.6) vd (t) vq (t) Where the angle θ is the transformation angle, which is also presented in Fig 2.2 (B.7) [...]... single generator and the power system It is not useful for studies of large power systems but it helps to understand the effect of the field, damper circuits and the excitation system in the dynamic response of a single generator [11] The SM-IB system model is also the base to analyze and to tune the PSS controller to enhance the dynamic stability of the generator through the excitation control system. .. presented in the complete and linearized models of the SM-IB system described in this chapter The linearized model will be a suitable model for PSS tuning while the complete one will allow to test the results reached from the PSS tuning process and from the application of other control structures to damp power oscillations in the power system The parameters of the test generator and the models used for the. .. comparing the measured terminal voltage with the reference voltage This error is processed to calculate a voltage reference signal for the excitation That reference alters the exciter output and thereby the generator field current, eliminating the terminal voltage error The exciter constitutes the power stage of the excitation system [11] It supplies the DC power to the field winding in the synchronous generator. .. equation of the synchronous machine combined with the external network equations to obtained the linearized state-space model of the Chapter 2 Synchronous Machine Infinite Bus Modelling system [11] For this model the state variables are the rotor angular speed, the rotor angular position and the field flux The voltage of the infinite bus is defined to be constant therefore there is no input for it in the model... system collapses On the other hand, in the synchronous generator, the damping that the field and damper windings provide to the rotor oscillations is weakened due to excitation control system action The reason for this is that in the rotor circuits appear additional currents induced by the voltage regulation and those currents oppose to the currents induced by the rotor speed deviations [18] Therefore,... In the model, the field flux is considered to be aligned to the d-axis, where there is also a damper winding 1d The other two damper windings 1q and 2q are placed in the q-axis The dq reference system is a rotating system and to express the stator circuit in Chapter 2 Synchronous Machine Infinite Bus Modelling the same reference, the dq Transformation is used, specifically Power Invariant Transformation... [11] The transformations equations for three phase systems are presented in Appendix B The angle θ in Fig 2.2 is the transformation angle and it represents the angle by which the d-axis leads the magnetic axis of the a-phase winding [11] Fig 2.2 Synchronous Machine Stator and Rotor Circuits The equations of the synchronous machine that are presented as follows are stated under generator convention for. .. suitable to analize the phase compensation that the PSS should provide to the system To add damping to the rotor oscillations, the PSS has to guarantee that the created torque component is in phase with the rotor speed deviations To achieve this it has to compensate the phase lag that the excitation system and the field circuit of the generator introduce between the excitation system input and the electrical... affect the electrical torque [11] Therefore, the rotor angle variation effect is eliminated from the model and in that way the rotor speed is kept constant The block diagram of the modified model, that will be called the Transient Model for system phase analysis and is used for investigating the phase lag in the system, is presented in Fig 2.9 Fig 2.9 Block Diagram SM-IB Transient Model for System. .. (2.48) (2.49) (2.50) (2.51) (2.52) The mathematical derivation above allow redrawing the block diagram of the system as is presented in Fig 2.10 This model is only suited for study the phase lag between the input to the excitation system and the resulting electric torque in the synchronous machine, under the assumption that the rotor speed is constant Chapter 2 Synchronous Machine Infinite Bus Modelling ... process and from the application of other control structures to damp power oscillations in the power system The parameters of the test generator and the models used for the excitation system are provided... of the electrical grids and in the worst case, risks of partial system collapses On the other hand, in the synchronous generator, the damping that the field and damper windings provide to the. .. Diagram of the SM-IB System The SM-IB system can be considered as a theoretical simple system that allows to study the electromechanical interaction between a single generator and the power system